CHAPTER 13 Textual Desert – Emotional Oasis: An unconventional ...

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• cours magistral

dr a f t   1 CHAPTER 13    Textual Desert – Emotional Oasis:   An unconventional confessional dialogue on field experience  Stevan Harrell and Li Xingxing  A confessional dialogue (Stevan Harrell)  The  two  essays  below  constitute  a  confessional  dialogue  between  two  anthropologists,  one  from the United States of America and the other from China, about an extended field project  that has yielded profound emotional connections but very little anthropological analysis. In his  witty  little  book  Tales  of  the  Field  (1988),  John  van  Maanen  distinguishes  three  kinds  of  ethnographic narratives: realist, confessional and  impressionist tales. The realist tale assumes  that  there  is an objective  reality of society and culture and attempts  to describe  them, using  ‘good' scientific field methods that will lead to good description, both true to the reality of the  people studied and useful in advancing the science of anthropology. The impressionist tale, on  the other hand, tends toward the  literary rather than the scientific, spinning a narrative from  the  fieldwork  experience  without  much  analysis  or  systematization,  and  little  or  no  generalization,  leaving  it  to  the  reader  to draw any  implications.

• upper  baiwu
• few  field 
• analysis  or  systematization
• if  i ask a  relatively complicated question
• i have the  linguistic qualifications to work  in baiwu
• it cannot avoid the topic of emotions experienced  in the  field
• yangjuan  primary  school 
• i either cannot get the question out or  i very awkwardly spit  out a pile of nouns and verbs
• from  confusion  and blunders to insight and understanding
• and 

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• Cours magistral
• Systematization (Romania)
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• Publié par: upsae
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 9 Mo

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NEW RESOLUTION STRATEGY FOR MULTI-SCALE REACTION
WAVES USING TIME OPERATOR SPLITTING, SPACE ADAPTIVE
MULTIRESOLUTION AND DEDICATED HIGH ORDER
IMPLICIT/EXPLICIT TIME INTEGRATORS
yz y x {MAX DUARTE , MARC MASSOT , STEPHANE DESCOMBES , CHRISTIAN TENAUD ,
k k y THIERRY DUMONT , VIOLAINE LOUVET , AND FREDERIQUE LAURENT
Abstract. We tackle the numerical simulation of reaction-di usion equations modeling multi-
scalereactionwaves. Thistypeofproblemsinducespeculiardi cultiesandpotentiallylargesti ness
whichstemfromthebroadspectrumoftemporalscalesinthenonlinearchemicalsourcetermaswell
as from the presence of steep spatial gradients in the reaction fronts, spatially very localized. In this
paper, we introduce a new resolution strategy based on time operator splitting and space adaptive
multiresolution in the context of very localized and sti reaction fronts. It considers a high order
implicit time integration of the reaction and an explicit one for the di usion term in order to build
a time operator splitting scheme that exploits e ciently the special features of each problem. Based
onrecenttheoreticalstudiesofnumericalanalysissuchastrategyleadstoasplittingtimestepwhich
is not restricted neither by the fastest scales in the source term nor by stability constraints of the
di usive steps, but only by the physics of the phenomenon. We aim thus at solving complete models
includingalltimeandspacescaleswithinaprescribedaccuracy,consideringlargesimulationdomains
withconventionalcomputingresources. Thee ciencyisevaluatedthroughthenumericalsimulation
ofcon gurationswhichweresofar,outofreachofstandardmethodsinthe eldofnonlinearchemical
dynamicsfor2Dspiralwavesand3Dscrollwavesasanillustration. Futureextensionsoftheproposed
strategy to more complex con gurations involving other physical phenomena as well as optimization
capability on new computer architectures are nally discussed.
Key words. Reaction-di usion equations, multi-scale reaction waves, operator splitting, adap-
tive multiresolution
AMS subject classi cations. 33K57, 35A18, 65M50, 65M08
1. Introduction. Numerical simulations of multi-scale phenomena are com-
monly used for modeling purposes in many applications such as combustion, chemical
vapor deposition, or air pollution modeling. In general, all these models raise several
di cultiescreatedbythehighnumberofunknowns,thewiderangeoftemporalscales
due to large and detailed chemical kinetic mechanisms, as well as steep spatial gra-
dients associated with very localized fronts of high chemical activity. Furthermore, a
natural stumbling block to perform 3D simulations with all scales resolution is either
the unreasonably small time step due to stability requirements or the unreasonable
memory requirements for implicit methods. In this context, one can consider var-
ious numerical strategies in order to treat the induced sti ness for time dependent
This research was supported by a fundamental project grant from ANR (French National Re-
search Agency - ANR Blancs) Sechelles (project leader S. Descombes - 2009-2013), by a CNRS
PEPS Maths-ST2I project MIPAC (project leader V. Louvet - 2009-2010), and by a DIGITEO
RTRA project MUSE (project leader M. Massot - 2010-2014).
yLaboratoire EM2C - UPR CNRS 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295
Ch^atenay-Malabry Cedex, France (fmax.duarte,marc.massot,[e-mail]).
zSupported by a Ph.D. grant from Mathematics (INSMI) and Engineering (INSIS) Institutes of
CNRS and by INCA project (CNRS/ONERA/SAFRAN).
xLaboratoire J. A. Dieudonne - UMR CNRS 6621, Universite de Nice - Sophia Antipolis, Parc
Valrose, 06108 Nice Cedex 02, France ([e-mail]).
{LIMSI - CNRS, B.P. 133, Campus d’Orsay, 91403 Orsay Cedex, France ([e-mail]).
kInstitut Camille Jordan - UMR CNRS 5208, Universite de Lyon, Universite Lyon 1, INSA de
Lyon 69621, Ecole Centrale de Lyon, 43 Boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex,
France (ftdumont,[e-mail]).
12 DUARTE, MASSOT, DESCOMBES, TENAUD, DUMONT, LOUVET, LAURENT
problems. The most natural idea is to use dedicated numerical methods and to solve
the complete models where di usion, reaction and eventually convection are coupled
together. One aims at solving strongly coupled nonlinear systems with either a fully
implicit method, or yet semi-implicit or linearized implicit methods instead (see [9]
and references therein). However, the strong stability restrictions for the latter when
dealing with very fast temporal scales, as well as the computing cost and the high
memory requirements of these methods, even if adaptive grids are used, make these
strategies di cult to be handled.
Analternativenumericalstrategyisthentocombineimplicitandexplicitschemes
to discretize nonlinear evolution problems in time. Further studies settled the appro-
priate numerical background for these methods called IMEX, which in particular
might be conceived to solve sti nonlinear problems [35, 29]. These methods are
usually very e cient but the feasibility of utilizing dedicated implicit solvers over a
discretized domain becomes soon critical when treating large computational domains.
On the other hand, the time steps globally imposed over partial regions or the entire
domain are strongly limited by either the stability restrictions of the explicit solver
or by the fastest scales treated by the implicit scheme. We know though that these
fastest time scales do not always play a leading role in the global physics of many
multi-scaleproblemsandthereforeonemightconsiderthepossibilityofusingreduced
models where these chemical scales have been previously relaxed. These simpli ed
models provide reasonable predictions and the associated computing costs are signif-
icantly reduced in comparison with comprehensive chemical models. Nevertheless,
these models provide only approximate solutions and are usually accessible
when the system is well-partitioned and the fastest scales can be identi ed or isolated
[30], a process that in realistic con gurations, relies on sensitivity analysis which is
most of the time di cult to conduct and justify.
It is then natural to envision a compromise, since the resolution of the fully
coupled problem is most of the time out of reach and the appropriate de nition
of reduced models is usually di cult to establish. In this context, time operator
splitting methods have been used for a long time and there exists a large literature
showing the e ciency of such methods for evolution problems. A splitting procedure
allows to consider dedicated solvers for the reaction part which is decoupled from the
other physicalphenomena likeconvection, di usion or both, for whichthere also exist
dedicated numerical methods. Hence, a completely independent optimization of the
resolution of each subsystem might be pursued. In order to guarantee the accuracy
of the solution obtained by a splitting scheme, the splitting time steps used for the
independentresolutionofeachsubproblemareusuallytakenoftheorderofthefastest
scales included in the problem. As a matter of fact, several works [36, 31, 9] showed
that the standard numerical analysis of splitting schemes fails in presence of scales
muchfasterthanthesplittingtimestep. Nevertheless, morerigorousstudiesforthese
sti con gurations [15, 13] and in the case where spatial multi-scale phenomena arise
as a consequence of steep spatial gradients [12], allow to characterize the behavior of
splitting schemes with splitting time steps much larger than the fastest scales of the
problem.
As a consequence, we introduce in this work a new time operator splitting ap-
proachforwhichthededicatedmethodschosenforeachsubsystemareresponsiblefor
dealing with the fast scales associated with each one of them, in a separate manner.
The global solution is then reconstructed by the splitting scheme with splitting time
steps dictated by the global physical coupling, possibly much larger than the fastestNEW RESOLUTION STRATEGY FOR MULTI-SCALE REACTION WAVES 3
time scales. In this way, the splitting time step is chosen based only on error esti-
mates of the numerical simulation in order to guarantee the description of the physics
of the phenomenon within a prescribed accuracy, without being related to the stabil-
ity constraints of the numerical resolution of each subsystem and with an important
improvement of e ciency whenever a broad decoupling of the time scale spectrum is
possible.
The operator splitting strategy proposed in this article considers then a high or-
der method like Radau5 [23], based on implicit Runge-Kutta schemes for sti ODEs,
to solve the reaction term; and on the other hand, another high order method like
ROCK4 [1], based on explicit stabilized Runge-Kutta schemes, to solve the di usion
problem. In this way, the global accuracy of the time integration scheme is mainly set
by the splitting scheme through the choice of the splitting time step. This numerical
strategyisthencomplementedbyameshre nementtechniquebasedonHarten’spio-
neering work on adaptive multiresolution methods [24], being aware of the interest of
adaptivemeshtechniquesforproblemsexhibitinglocallysteepspatialgradients. Since
a multiresolution technique allows to better control the accuracy of the adapted and
compressedspatialrepresentation,boththespaceandtimeerrorscanberegulatedfor
a given semi-discretized problem. The main goal is then to perform